[N,k,chi] = [6005,2,Mod(1,6005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
\( p \) |
Sign
|
\(5\) |
\(-1\) |
\(1201\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{88} + 14 T_{2}^{87} - 23 T_{2}^{86} - 1205 T_{2}^{85} - 2777 T_{2}^{84} + 47070 T_{2}^{83} + 207654 T_{2}^{82} - 1068382 T_{2}^{81} - 7279036 T_{2}^{80} + 14221060 T_{2}^{79} + 166802742 T_{2}^{78} + \cdots + 32 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6005))\).